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A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

Guest Feb 22, 2018

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 #1
avatar+19370 
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A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

 

\(\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{$3\ $spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array} \)

 

\(\text{$\frac13$ of the cylinder is not filled by the spheres.} \)

 

laugh

heureka  Feb 22, 2018
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 #1
avatar+19370 
+1
Best Answer

A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

 

\(\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{$3\ $spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array} \)

 

\(\text{$\frac13$ of the cylinder is not filled by the spheres.} \)

 

laugh

heureka  Feb 22, 2018

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